2. Jeremiah\'s Pub is a neighborhood tavern located on Monroe Avenue in Rocheste

Question

2. Jeremiah's Pub is a neighborhood tavern located on Monroe Avenue in Rochester. It is locally or its friendly atmosphere and world class chicken wings. There are 4 consecutive parking spaces on the st of the pub and has collected highly reliable data on how often the spaces are occupied. She estimates that, at any given time, the probability that a space is occupied is .8. Assume that occupation of any space is independent of the occupation of the other spaces eet directly in front of the establishment. Ana O. is a frequent patron (5) How many arrangements of occupied/unoccupied spaces are there for this scenario ? (5) What is the probability that all of the spaces are occupied at the same time ? (5) What is the probability that exactly two of the spaces are occupied at any given time? (10) Charley G. is also a regular customer at Jeremiah's. However, Charley is a lousy driver and is unable to park in front of the facility unless there are at least two consecutive empt spaces available. Enumerate the possible arrangements that meet this requirement and compute the probability that Charley can park in front of the pub.

Explanation / Answer

1) Parking Space P-1 P-2 P-3 P-4

[ 0 : Unoccupied , 1 : Occupied ]

2) (0.8)*(0.8)*(0.8) *(0.8) = 0.4096

3) (0.8)*(0.8) = 0.64

4) There are seven possible arrangements that meet his requirement.

The probability that Charlie can park in front of the pub is given by (0.2)*(0.2)*(0.2) = 0.008

S No P-1 P-2 P-3 P-4 1 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 0 1 6 0 1 1 0 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1 10 1 0 1 0 11 1 0 1 1 12 1 1 0 0 13 1 1 0 1 14 1 1 1 0 15 1 1 1 1

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